Symmetry: modeling the effects of masking noise, axial cueing and salience

Abstract

Symmetry detection is an interesting probe of pattern processing because it requires the matching of novel patterns without the benefit of prior recognition. However, there is evidence that prior knowledge of the axis location plays an important role in symmetry detection. We investigated how the prior information about the symmetry axis affects symmetry detection under noise-masking conditions. The target stimuli were random-dot displays structured to be symmetric about vertical, horizontal, or diagonal axes and viewed through eight apertures (1.2 degrees diameter) evenly distributed around a 6 degrees diameter circle. The information about axis orientation was manipulated by (1) cueing of axis orientation before the trial and (2) varying axis salience by including or excluding the axis region within the noise apertures. The percentage of correct detection of the symmetry was measured at for a range of both target and masking noise densities. The threshold vs. noise density function was flat at low noise density and increased with a slope of 0.75-0.8 beyond a critical density. Axis cueing reduced the target threshold 2-4 fold at all noise densities while axis salience had an effect only at high noise density. Our results are inconsistent with an ideal observer or signal-to-noise account of symmetry detection but can be explained by a multiple-channel model is which the response in each channel is the ratio between the nonlinear transform of the responses of sets of early symmetry detectors and the sum of external and intrinsic sources of noise.

Figure 1. Examples of stimuli.

A. The configuration consisted of an overall noise pattern with a single axis orientation visible through a mask of eight apertures The axial salience was controlled by the position of the apertures, located so as to either include or exclude the region around the axis. B. Examples of different combinations of target and masker density.

Figure 2. Target threshold vs. masker density functions.

Each panel represents data from one observer. Blue denotes the TvD function for the cued high salience condition; magenta, the cued low salience condition; green, the non-cued high salience condition; and red, the non-cued low salience condition. The smooth curves are fits of the model discussed below. The error bars are the estimated standard error of measurement.

Figure 3. The average threshold change produced by cueing (open circles) and axial salience (closed circles) at different masker densities.

The dashed and dotted blue lines indicate the predictions of the uncertainty model and the signal-to-noise, or weight-of-evidence, model respectively.

Figure 4. The slopes of the TvD functions.

The solid lines have a slope of 1, the dashed lines, a slope of 0.75. The lines with unity slope tend to overestimate thresholds at high masker density and underestimate them at low masker density.

Figure 5. Diagram of the model.

A. Without cues. B. With cues. See text for details.

Figure 6. Examples of the model parametrization.

The black curve has all three model components in the denominators, with parameters chosen to for a strong double-corner effect. Green curve: removing the internal noise reduces the threshold at low masker density. Blue curve: removing the divisive inhibition limits the masking effect at high masker density. (Removing the external noise results in a horizontal line, since it is the parameter of the x axis.)